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Integrability of Green potentials in fractal domains
Authors:Kaj Nyström
Affiliation:1. Department of Mathematics, University of Ume?, S-90187, Ume?, Sweden
Abstract:We proveL q -inequalities for the gradient of the Green potential (Gf) in bounded, connected NTA-domains inR n ,n≥2. These domains may have a highly non-rectifiable boundary and in the plane the set of all bounded simply connected NTA-domains coincides with the set of all quasidiscs. We get a restriction on the exponentq for which our inequalities are valid in terms of the validity of a reverse Hölder inequality for the Green function close to the boundary.
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